A swivel‐jointed formalism for segmentally flexible macromolecules and its application to the rotational behavior of myosin

A formalism is presented to represent the hydrodynamic and diffusion behavior of segmentally flexible macromolecules with a high degree of flexibility. The development specifically treats open assemblies of cylindrically symmetric segments joined at their end points by frictionless swivels. Three‐dimensional diffusion and frictional tensors that govern the rotations of each segment and the translations of some chosen swivel are established and related by a Stokes–Einstein relation. The dependence of these tensors on the choice of swivel is examined, and simplified expressions are obtained by omitting hydrodynamic interactions between segments. These simplified expressions are used to analyze the rotational behavior of a Y‐shaped body in detail. If there is complete flexibility, the rotational motions of each segment reduce, for all practical purposes, to those of a cylindrically symmetric rigid body. Estimates are provided to relate segment rotations to internal motions and restrictions on flexibility. A procedural framework for generating rotational diffusion coefficients for segments of more complicated bodies is applied to a four‐segment two‐swivel myosin model. Comparison of calculated and experimental relaxation times for myosin and its fragments indicates the head–tail junction is highly flexible, with at least a ±60° angular extent of free bending between heads allowed, while the tail is neither straight and rigid nor highly flexible.